1. Logical Reasoning in Geometry
Unit 4
Logical Reasoning in Geometry

2. Pre Day- Vocabulary

3. Define these terms! Line Segment Perpendicular Lines Coplanar Midpoint
Bisect
Non-collinear
Plane
Parallel Lines
Skew Lines
Non-coplanar
Collinear

4. Matching (in packet) Complete the matching activity
Bring it up to the front to check answers when done
Draw examples of each word in the blank the bottom of the page in packet

5. Flip Book
We’re going to make a flip book that looks just like the picture
Each person needs 3 pieces of paper
Every group needs 1 pair of scissors
You will need something
to write with. I
recommend using a
pencil for the inside and
perhaps a marker for the
outside tab

6. Flip Book Cover Page: Unit 4 FoM 3 Reasoning in Geometry
Label each tab as follows:
We will fill in the booklet each day
Midpoint
Complimentary Angles
Segment Addition Postulate
Perpendicular Bisector
Angle Addition Postulate
Vertical Angles
Bisectors
Supplementary Angles
Perpendicular Lines
Angles & Parallel Lines

7. Using Definition of Midpoint
Day 1
Using Definition of Midpoint

8. Warm Up Day 1

9. Don’t assume midpoint! You must be told!
Def: Midpoint
The midpoint of a line segment divides the line segment into two congruent segments. A B M 1) 3) 5) 2) 4) 6)
Don’t assume midpoint! You must be told!

10. Flipbook

11. Let’s do the evens!

12. Now you try the odds!

13. 1.1 Guided Practice in packet
Turn in Example 2 and Example 3 as ET on half sheet of paper before leaving

14. Segment Addition Postulate
Day 2
Segment Addition Postulate

15. Warm Up Day 2

16. Let’s think…
How would I measure the floor length of this classroom with a 12 inch ruler?
I’d like 3 volunteers to measure please!
That’s basically the segment addition postulate!

17. Addition and Subtraction of Line Segments:
If several line segments belong to the same line, we can write addition and subtraction expressions using the names of these segments. R P S
Geometry Leeson: Undefined Terms, Lines, Line Segments

18. Flipbook

19. 1.2 Guided Practice Ex
In packet!

20. Stations
Complete the stations on a separate piece of paper and have them checked by me before you leave!

21. Angle Addition Postulate
Day 3
Angle Addition Postulate

22. Warm Up Day 3 If Q is the midpoint of … 1) What is the value of x?
2) What is the measure of
3) What is the measure of ? Q

23. Review Naming Angles

24. Angle Addition Postulate
First, let’s recall some previous information from last week….
We discussed the Segment Addition Postulate, which stated that we could add the lengths of adjacent segments together to get the length of an entire segment.
For example:
JK + KL = JL
If you know that JK = 7 and KL = 4, then you can conclude that JL = 11.
The Angle Addition Postulate is very similar, yet applies to angles. It allows us to add the measures of adjacent angles together to find the measure of a bigger angle… J K L

25. Angle Addition Postulate
Slide 2
If B lies on the interior of ÐAOC,
then mÐAOB + mÐBOC = mÐAOC. B A
mÐAOC = 115°
50°
65° C O

26. Flipbook

27. A B C D G K H J 134° 46° 46 Given: mÐGHK = 95 mÐGHJ = 114.
Example 1:
Example 2:
Slide 3 G
114° K
46°
95°
19° H
This is a special example, because the two adjacent angles together create a straight angle.
Predict what mÐABD + mÐDBC equals.
ÐABC is a straight angle, therefore mÐABC = 180.
mÐABD + mÐDBC = mÐABC
mÐABD + mÐDBC = 180
So, if mÐABD = 134,
then mÐDBC = ______ J
Given: mÐGHK = 95
mÐGHJ = 114.
Find: mÐKHJ.
The Angle Addition Postulate tells us:
mÐGHK + mÐKHJ = mÐGHJ
95 + mÐKHJ = 114
mÐKHJ = 19.
Plug in what you know. 46
Solve.

28. Set up an equation using the Angle Addition Postulate.
Given:
mÐRSV = x + 5
mÐVST = 3x - 9
mÐRST = 68
Find x.
Algebra Connection
Slide 4 R V
Extension: Now that you know x = 18, find mÐRSV and mÐVST.
mÐRSV = x + 5
mÐRSV = = 23
mÐVST = 3x - 9
mÐVST = 3(18) – 9 = 45
Check:
mÐRSV + mÐVST = mÐRST
= 68 S T
Set up an equation using the Angle Addition Postulate.
mÐRSV + mÐVST = mÐRST
x x – 9 = 68
4x- 4 = 68
4x = 72
x = 18
Plug in what you know.
Solve.

29. x – 7 + 2x – 1 = 2x + 34 3x – 8 = 2x + 34 x – 8 = 34 x = 42 x = 42 C B
mÐBQC = x – 7 mÐCQD = 2x – 1 mÐBQD = 2x + 34
Find x, mÐBQC, mÐCQD, mÐBQD. C B
mÐBQC = x – 7
mÐBQC = 42 – 7 = 35
mÐCQD = 2x – 1
mÐCQD = 2(42) – 1 = 83
mÐBQD = 2x + 34
mÐBQD = 2(42) + 34 = 118
Check:
mÐBQC + mÐCQD = mÐBQD
= 118 Q D
mÐBQC + mÐCQD = mÐBQD
x – 7 + 2x – 1 = 2x + 34
3x – 8 = 2x + 34
x – 8 = 34
x = 42
x = 42
mÐBQC = 35
mÐCQD = 83
mÐBQD = 118
Algebra Connection
Slide 5

30. 1.3 Practice: Coach/Student
One person is the coach, other is student
Complete 1 & 2
Swap roles
Complete 3 & 4
Reflect – which role was more difficult for you to fill? Why would that be true?

31. Exit Ticket – ½ sheet

32. Day 4
Bisectors

33. Warm Up
Top section of Warm Up 1.4 in packet

34. Midpoint The point that bisects a segment. Bisects?
splits into 2 equal pieces
A M B
12x x+5
12x+3=10x+5
2x=2
x=1

35. Segment Bisector
A segment, ray, line, or plane that intersects a segment at its midpoint. k A M B

36. Angle Bisector
A ray that divides an angle into 2 congruent adjacent angles.
BD is an angle bisector of <ABC. A D B C

37. Flipbook

38. Ex: If FH bisects EFG & mEFG=120o, what is mEFH?

39. Last example: Solve for x.
* If they are congruent, set them equal to each other, then solve!
x+40o
x+40 = 3x-20
40 = 2x-20
60 = 2x
30 = x
3x-20o

40. 1.4 Guided Practice

41. Day 5
Review and Quiz 4A

42. Warm Up Day 5 – round robin
On your WU paper, copy your problem. Draw a picture if needed then set up an equation to solve.
Pass your paper to left. Verify the equation, fix if needed. Then solve for x.
Pass left. Verify value of x by plugging in, fix if needed. Then find lengths.
Pass left. Check over all work, fix if needed. Kudos!

43. LMR - quiz

44. Day 6
Right Angles

45. Warm Up Day 6

46. Right Angles What are right angles? How are they formed?
Why are they important?
Find examples of right angles around the room.

47. Perpendicular Lines
“Perpendicular lines are special intersecting lines that form right angles (square corners) where they intersect.”

48. Flipbook

49. 1.5 Guided Practice in packet

50. Day 6
Angle Relationships

51. Warm Up Day 6

52. Flipbook

53. 1-2-3-6-7-8 Work your assigned problem as a group You have 5 minutes
Now Jigsaw around the room – become a master of all!
Random members will share on board

54. Exit Ticket

55. Supplementary Angles and Linear Pairs
Day 7
Supplementary Angles and Linear Pairs

56. Warm Up Day 7

57. Video on Supplementary Angles and Linear Pairs
Watch me if you need a bit of help!

58. 1.7 Guided Practice
Musical Groups!

59. 1.7 Practice
Silent, individual practice today to ensure everyone in the classroom is confident!

60. Day 8
Parallel Lines

61. Warm Up Day 8
Solve for the numbered angles.

62. Parallel Lines and Transversals
What would you call two lines which do not intersect?
Parallel
A solid arrow placed on two lines of a diagram indicate the lines are parallel.
Exterior
Interior
The symbol || is used to indicate parallel lines.
Exterior
AB || CD

63. Transversal
A line, ray, or segment that intersects 2 or more COPLANAR lines, rays, or segments.
transversal
Exterior
Exterior
transversal
Parallel lines
Non-Parallel lines
Interior
Interior
Exterior
Exterior

64. Corresponding Angles ÐGPB = ÐPQE ÐGPA = ÐPQD ÐBPQ = ÐEQF ÐAPQ = ÐDQF
When two parallel lines are cut by a transversal, pairs of corresponding angles are formed.
Line M B A
Line N D E L P Q G F
Line L
ÐGPB = ÐPQE
ÐGPA = ÐPQD
ÐBPQ = ÐEQF
ÐAPQ = ÐDQF
Four pairs of corresponding angles are formed.
Corresponding pairs of angles are congruent.

65. Alternate Interior Angles
Alternate angles are formed on opposite sides of the transversal and at different intersecting points.
Line M B A
Line N D E L P Q G F
Line L
ÐBPQ = ÐDQP
ÐAPQ = ÐEQP
Two pairs of alternate angles are formed.
Pairs of alternate angles are congruent.

66. Exit Ticket 1. Name the angles congruent to 3. 1, 5, 7
2. Name all the angles supplementary to 6.
In the figure a || b.
1, 3, 5, 7
3. If m1 = 105° what is m3?
105°
4. If m5 = 120° what is m2?
60°